Ryota Akagi

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math.RT2026

Real $C$ -, $G$ -structures and sign-coherence of cluster algebras

Ryota Akagi, Zhichao Chen

We generalize the theory of integer $C$ -, $G$ -matrices in cluster algebras to the real case. By a skew-symmetrizing method, we can reduce the problem of skew-symmetrizable patterns…

math.RT2026

Fractal phenomenon in $c$ - and $g$ -vectors of the Markov quiver

Ryota Akagi, Zhichao Chen

We study the $C$ - and $G$ -patterns associated with rank $3$ skew-symmetrizable matrices of $B$ -invariant type, including the Markov quiver. Motivated by the self-contained simple m…

math.RT2026

Relation between generalized and ordinary cluster algebras

Ryota Akagi, Tomoki Nakanishi

Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their i…

Real C-, G-structures and sign-coherence of cluster algebras

Fractal phenomenon in c- and g-vectors of the Markov quiver

Relation between generalized and ordinary cluster algebras

Real $C$ -, $G$ -structures and sign-coherence of cluster algebras

Fractal phenomenon in $c$ - and $g$ -vectors of the Markov quiver